Significant Figures
A measurement carries a claim about its own precision. Significant figures are how that claim is written down - and how it survives a calculation.
Last updated: August 2026 · Written and verified by Akash Pandey
Which digits are significant
| Rule | Example | Sig. figs |
|---|---|---|
| All non-zero digits count | 4,271 | 4 |
| Zeros between non-zero digits count | 3,004 | 4 |
| Leading zeros never count | 0.0042 | 2 |
| Trailing zeros after a decimal point count | 2.500 | 4 |
| Trailing zeros in a whole number are ambiguous | 1,500 | 2, 3 or 4 |
| Scientific notation removes the ambiguity | 1.50 × 10³ | 3 |
That last pair is the reason scientific notation matters beyond compactness. Written as 1500, there is no way to know whether the zeros were measured or are placeholders. Written as 1.5 × 10³ it is unambiguously two significant figures; as 1.500 × 10³, four.
Rounding
- Identify the digit at the position you are rounding to.
- Look at the single digit immediately to its right.
- If that digit is 5 or more, round up; if 4 or less, leave it.
- Replace everything to the right with zeros, or drop it if it is past the decimal point.
Round 3.14159 to 3 significant figures
3.14159 → 3 s.f.
- The first three significant digits are 3, 1 and 4.
- The next digit is 1, which is below 5.
- So the 4 stays as it is.
= 3.14
Round 0.0027856 to 3 significant figures
0.0027856 → 3 s.f.
- Leading zeros do not count, so the first significant digit is 2.
- Three significant digits gives 2, 7, 8.
- The next digit is 5, so round the 8 up to 9.
= 0.00279
Round 149,600 to 2 significant figures
149600 → 2 s.f.
- The first two significant digits are 1 and 4.
- The next digit is 9, so round the 4 up to 5.
- Zeros hold the place value: 150,000. Writing it as
1.5 × 10⁵makes the precision explicit.
= 150,000 or 1.5 × 10⁵
Carrying precision through a calculation
A result can never be more precise than the least precise number that went into it. The rule differs by operation:
| Operation | Governed by | Example |
|---|---|---|
| Multiply / divide | Fewest significant figures | 2.5 × 3.42 = 8.6 (2 s.f.) |
| Add / subtract | Fewest decimal places | 12.11 + 1.2 = 13.3 (1 d.p.) |
| Logarithms | Sig figs of input → decimal places of output | log(2.0 × 10³) = 3.30 |
| Exact counts | Unlimited precision | 3 apples is exactly 3 |
Exact values - counted quantities, defined constants, conversion factors like 100 cm in a metre - impose no limit. Only measurements do.
Frequently Asked Questions
How many significant figures does 0.00500 have?
Three. The leading zeros are placeholders and do not count, but the trailing zeros after the decimal point do, because they communicate measured precision.
Do trailing zeros in a whole number count?
It is ambiguous without more information. 1500 could be two, three or four significant figures. Write it in scientific notation to say which you mean.
Should I round at every step of a calculation?
No. Rounding intermediate values compounds error. Keep full precision throughout and round only the final answer.
What is the difference between significant figures and decimal places?
Decimal places count digits after the point; significant figures count meaningful digits wherever they fall. 0.00420 has five decimal places but three significant figures.
What is banker's rounding?
Rounding a half to the nearest even digit, so 2.5 becomes 2 and 3.5 becomes 4. It removes the upward bias of always rounding halves up, and is common in finance and statistics.